March 8, 2018

Presentation Structure

  • Introduction to the present project
  • Objectives of the current research
  • Background and Context
  • Research Questions
  • Data sources
  • Methods - Spatial data are special!
  • Methods - The INLA approach to Bayesian analysis
  • Results & visualizations
  • Wrap up and current work

Introduction to the present project

  • Women in Latin America face violence in many form in daily life
    • Daughters, sisters, wives; working or retired
  • Machismo and Marianismo are cultural traditions found throughout Latin America
    • Stress the persistent conflict between being "manly" and being "pure and passive"
    • Often leads to conflict within households & domestic violence
    • Absolutely not unique to Latin America

Introduction to the present project

  • La cultura de violencia
  • In Mexico, 44% of women have suffered some type of violence from their partner. Report
  • This often results in some form of internal displacement for women and men
    • Attempting to leave this violence behind and seek asylum
    • Women are often targeted for violence by cartels or gangs

Introduction to the present Project

  • Spatial poverty traps
    • Areas where poverty is persisently high over both time and space
    • These are areas where physical, natural, social, political, and human capital is low and poverty is high
    • Different disciplines provide large amount of evidence on linking poverty and gender based violence
  • The contextual factors related to gender based violence are not only socioeconomic factors
    • Such as poverty or low education
    • Also include cultural and demographic patterns mainly in some rural or remote areas of the country

Objectives of the current research

  • Provide insights into the association between poverty in Mexico and gender-based violence
  • Identify significant concentrations of high poverty rates and high incidence of gender based violence

Research Questions

  • Are poverty and female homicide co-incident in Mexico?
  • Is this relationship stationary over time and space?

Data

  • The information for homicides comes from the vital statistics of the Instituto Nacional de Estadistica y Geografia (INEGI)
    • These data are individual death records
    • Using ICD-10 codes, we isolate female homicides (ICD-10: X85-Y09)
    • Between years 1995 and 2015: a total of 15,108 homicides
    • Construct homicide rates by age (5 year age categories), year and municipio of occurrence
    • This generates a total of 1,759,248 rates over the period of study
    • Standardize all age-specific rates to Mexican national age structure in 2010 and sum rates within municipio and year to arrive at age-standardized rates

Data - Some Totals over Time

  • Total homicide rates over time

Data - Some Totals over Time - Male and Female Homicide

Data - National Picture over space

Data - National Picture over space

Data - National Picture over space

Spatial variation in poverty

1990 Poverty Rates

Spatial variation in poverty

2010 Poverty Rates

State Examples

*Chihuahau over time

Data - Variables

  • Several indicators are used in the analysis to control for physical and socioeconomic environment of municipios
    • Distance to US border
    • Poverty quartile
    • Migration intensity
    • % of population with incomplete primary school
    • Masculinity index
    • % population that is married
    • Average age at first union
    • Altitude

Methods - Hierarchical Model

  • I specify a Bayesian Hierarchical model for the standardized mortality ratio

  • \[Y_{ij} \sim \text{NegBin} (\lambda_{ij} \text{E}_{ij}, \lambda+\lambda^2/\theta)\]
  • \[ln \lambda_{ij} = \beta_{0} + x'\beta +\text{poverty}_i*\text{time}_t+\gamma_j*poverty_i + u_j + v_j\]
  • \[\gamma_1*\text{time} + \gamma_2* \left ( \text{time} * poverty_i \right )+\gamma_3*(\text{time} * seg_i)\]
  • \[\gamma_j \sim \text{CAR}(\bar \gamma_j, \tau_{\gamma}/n_j)\]
  • \[u_j \sim \text{CAR}(\bar u_j, \tau_u /n_j)\]
  • \[v_j \sim \text{N}(0, \tau_v )\]

  • Vague Gamma priors for all the \(\tau\)'s
  • Vague Normal priors for all the fixed effect \(\beta\)'s and \(\gamma\)'s

Methods - Bayesian analysis

  • This type of model is commonly used in epidemiology and public health
  • Various types of data likelihoods may be used
  • Need to get at:

*\[p(\theta|y) \propto p(y|\theta)p(\theta)\]

  • Traditionally, we would get \(p(\theta|y)\) by:
    • either figuring out what the full conditionals for all our model parameters are (hard)
    • Use some form of MCMC to arrive at the posterior marginal distributions for our parameters (time consuming)

Methods - INLA approach

  • Integrated Nested Laplace Approximation - Rue, Martino & Chopin (2009)
  • One of several techniques that approximate the marginal and conditional posterior densities
    • Laplace, PQL, E-M, Variational Bayes
  • Assumes all random effects in the model are latent, zero-mean Gaussian random field, \(x\) with some precision matrix
    • The precision matrix depends on a small set of hyperparameters
  • Attempts to construct a joint Gaussian approximation for \(p(x | \theta, y)\)
    • where \(\theta\) is a small subset of hyper-parameters

Methods - INLA approach

  • Apply these approximations to arrive at:
  • \(\tilde{\pi}(x_i | y) = \int \tilde{\pi}(x_i |\theta, y)\tilde{\pi}(\theta| y) d\theta\)

  • \(\tilde{\pi}(\theta_j | y) = \int \tilde{\pi}(\theta| y) d\theta_{-j}\)

  • where each \(\tilde{\pi}(. |.)\) is an approximated conditional density of its parameters

Methods - INLA approach

  • Approximations to \(\pi(x_i | y)\) are computed by approximating both \(\pi(\theta| y)\) and \(\pi(x_i| \theta, y)\) using numerical integration to integrate out the nuisance parameters.
    • This is possible if the dimension of \(\theta\) is small.
  • Approximations to \(\tilde{\pi}(\theta|y)\) are based on the Laplace appoximation of the marginal posterior density for \(\pi(x,\theta|y)\)
  • Their approach relies on numerical integration of the posterior of the latent field, as opposed to a pure Gaussian approximation of it

Model Results

  • Protective effects on female homicide risk: Shorter distance to border, Higher level of education, higher proportion married, older age at first union
  • Risk factors: High poverty areas farther from the US border

  • General hypothesis tests: Poverty displays a constant risk factor for female homicide over time - consistent temporal effect
  • Poverty displays little variation in how it impacts female homicide over space - consistent spatial effect

Spatial results

Spatial results

Discussion

  • There are several persistent areas of spatial clustering in the northwest of the country
    • Chihuahua, Durango and Sinaloa
    • as well as the southwest in states of Oaxaca, Michoacan, Gurrero and Estado de Mexico.
  • No space-time significance of poverty
  • Poverty is time invariant

Next steps

  • Current work is focusing on estimating influence of violence on life expectancy over time
  • Multi-level analysis focusing on incorporating individual level factors with contextual information
  • Exploring other causes of death in the data for spatial and temporal patterns

Thank you!

space

INLA in R

library(INLA)

f3n<-inla(formula = hfemale.x~scale(loc100_km)*factor(pa_q)+scale(migraes) +scale(priminc)+scale(imasc)+scale(pobcas)+scale(edadun)+factor(year)*factor(pa_q) +scale(altitud)+ f(struct, model="bym", graph = "MxMun.graph")+ f(struct2, pa_scale, model="iid") ,family = "nbinomial", E =e_fem+.00001, data = indat)